I cant extrude in Z Axis
Don't press G

The E shortcut is for the "Extrude Region and Move".



The move (or grab) command you are trying to recall with G is alredy active. So by pressing G, you are activating the Vertex Slide option of the grab command.

Just press E and then Z to restrict the movement because you are already grabbing the object around.

Or yuo can press E and then Esc to Extrude the region only. After that you can activate the grabbing with G and restrict the movement with Z.